1. Field of the Invention
The invention relates to systems and methods for modeling the behavior of a lithographic scanner and, more particularly, to systems and methods of using thresholds of an image profile to characterize printing behavior of a lithographic scanner.
2. Background Description
Any lithographic scanner takes a pattern on a mask, projects it through the lens, and makes an aerial image at the wafer plane. Because the lens can only collect finite orders of diffracted light and the lens is not perfect, the aerial image looks distorted when compared to the mask image. This is shown representatively in FIG. 1, for example. In order to obtain the desired image, chip makers typically make corrections on a reticle to adjust for optical proximity effects (OPE) for a specific scanner. This is a time consuming and costly process.
As Optical Proximity Correction (OPC) has enjoyed increased use, it has been recognized that a variety of lithographic parameters can strongly affect the OPC behavior of a scanner. Anecdotes abound in the industry, with tales of carefully-crafted OPC solutions suddenly failing to work when a process is run on a scanner made by a different manufacturer, or on a scanner made by the same manufacturer but with a different lens, or even on the same machine with different laser parameters. Given that OPC solutions require a considerable amount of time and effort to develop, this can be very disturbing.
OPC exists because of OPE. The purpose of OPC is to make the printed feature appear more like the designed feature, i.e., to negate OPE. In turn, the existence of OPE lies, of course, in the basic optical physics of image formation, especially at low k1 factors. Details of the optical design of the scanner have effects on the image formation and thus on OPE. This is frequently characterized by sets of data called OPE curves.
Drivers of OPE differences among scanners are broadly divided into two families. The first family of drivers is related to changes in lens NA (LNA), illuminator NA (INA) or annular ratio (AR). Those of skill in the art will recognize that the LNA and INA settings are frequently combined to calculate a term “sigma,” where sigma=INA/LNA. Since the image in the scanner is formed by combining the 0, ±1, and ±2 . . . diffraction orders in the lens, an image of the pupil-fill illumination pattern appears at the location of those orders in the lens pupil, and since some orders are cut off by the lens NA limits, small changes in LNA or INA or differences in the pupil-fill intensity pattern will subtly affect imaging. Through-pitch behavior can also be strongly affected.
A second family of drivers arises primarily from chromatic aberration in the lens and the non-infinitesimal bandwidth of the illumination laser. All lithographic lenses are made of glass and crystalline materials that are dispersive and, as such, every lens will thus have a characteristic change in aberrations as the incident wavelength is varied. Lasers, on the other hand, are not truly monochromatic but instead have a certain center wavelength and bandwidth. Thus, at any given time, the lens is projecting not a single image, but rather a composite of several images, each formed at a different wavelength and therefore with a slightly different set of lens aberrations. The composite is made by integrating these multiple images over the laser bandwidth. Typically, since the primary aberration affected by wavelength shift is focus, this corresponds to combining a best-focus image with a selection of out-of-focus images.
Bandwidth differences and lens differences from one scanner to another will also cause OPE differences between scanners. Other methods of introducing composite image formation, such as deliberate stage tilt induced to perform focus drilling, will similarly have OPE effects. In matching tools, adjustments of laser bandwidth or focus drilling are used for compensation of these effects.
The invention is designed to solve one or more of the above-mentioned problems.